submerged. Correct the weight found above for the buoyancy of the air, and the volume for the dilatation of the water, as in Experiment 19. Only in this case the whole weight of the displaced air must be added, since by definition the weight must be taken in vacuo. The density D of the water at any ordinary temperature. t, is given by the formula D = 1 − .000006 (t 4)2, its density at 4° being unity. After applying these two corrections, see if the volume of the water in cm3 equals its weight in grammes.

By using English weights and measures instead of French, the relation between the inch and pound may be established in a similar manner.

45. HYDROMETERS.

Apparatus. This consists of four tall jars, two containing water, the third some light liquid, as alcohol, and the fourth a saturated solution of salt, or other heavy liquid. A variety of hydrometers, some giving the specific gravity directly, others with the scales of Beaumé, Cartier and Beck, &c. In one of the jars of water, which should be larger than the other, is a Nicholson's hydrometer, Fig. 40, and on the table a box of weights, a small stone and a piece of hard wood. Near by should be a sink, with a large jar in it, through which water is continually flowing, to wash the hydrometers.

Experiment. Float each hydrometer in turn in the jar containing water, and record the reading of the point of the scale on its stem just at the surface. This point is determined most accurately by bringing the eye nearly on a level with the top of the water, but a little below it. All should give a specific gravity of very nearly unity, the difference being partly due to error in the instrument, and partly to expansion of the water by heat. Next immerse each in the alcohol, take the reading and wash by plunging it in the large vessel of water. Do the same with the solution of salt. If any hydrometer sinks lower than the top of its scale, the liquid is lighter than it can measure; if it floats too high the liquid is too heavy. Finally, reduce all the readings to specific gravities by the hydrometer tables. These instruments being of glass are easily broken, and must be handled with care.

Turning now to the Nicholson's hydrometer, place weights on the upper scale-pan A, until it sinks to the mark scratched on its

stem. Record their sum, and replace them in their box, taking care (as must always be done with delicate weights) never to touch them with the fingers, but only with forceps. Moreover they must never be laid down on the table, and to prevent their falling into the water, the piece of metal C must be kept over the mouth of the jar. Place the stone, or other object whose specific gravity is to be measured, on A, and add weights, as before. Call their sum in the first case w, in the second w'. Raise

the hydrometer out of the water (of course first replacing the weights in their box), and place the stone on the lower scale-pan B. Immerse it, taking care that there are no adhering air bubbles. If these cannot be detached with the finger, remove the stone and wash it first with caustic soda, and then with pure water. Call w" the weight required to immerse the hydrometer when the stone is on B. Then w”

is the apparent diminution of weight of the stone when immersed, or the weight of an equal bulk of water. As w―w' is the weight

of the stone, its specific gravity is

20

w'

w"

го

Perform the same

experiment with the piece of wood, only placing it below B to keep it down, and noticing that w" will be greater than w.

46. SPECIFIC GRAVITY BOTTLE.

Apparatus. A balance weighing up to 100 grms., and turning with two or three milligrammes, a set of weights and a specific gravity bottle, or as a substitute, two glass stoppered bottles, the neck of one being large, of the other, small. They should be carefully selected, with stoppers fitting smoothly, and a scratch should be made both on the neck and stopper, so that the latter may always be turned into the same position. As objects for determination of specific gravity any liquid may be used, as a solution of salt, and two or three solids, as stones, coins, gold ornaments, sand, &c.

Experiment. Weigh the empty bottle and stopper, and call their weight w. Fill the bottle with water, insert the stopper and wipe off the liquid which has overflowed, taking care that the exterior of both bottle and stopper are perfectly dry. Call this weight ww.

Fill with the liquid to be tested in the same way, taking care that the stopper is inserted in the same position as before, and that no liquid adheres to the exterior. Let the weight be w, then w1w and ww are the weights of equal bulks of the liquid

ալ w, a

a

and of water, and the specific gravity of the liquid is

W

To find the specific gravity of a solid, use the bottle with the larger neck. Call w the weight of the solid, w the weight of the bottle filled with water, and w, the weight when the solid is inserted, and the remaining space filled with liquid; then w+ww, equals the weight of a volume of water equal to that of the solid, and the specific gravity: This method is

го

w + ww

W

applicable to solids heavier or lighter than water. The principal precaution is to take care that no bubbles adhere to the solid or sides of the bottle, and that the stopper is always pressed in by the same amount. Use the same devices for removing the air as with the Nicholson's hydrometer, Experiment 45. With metals these precautions are especially important, or large errors will be introduced. Another good method is to place the flask containing the solid and water under the receiver of an air-pump and exhaust two or three times. This method is not applicable to wood, as it removes the air from the cells, and increases the apparent specific gravity. The same effect is produced by long immersion, and finally when waterlogged, the specific gravity becomes greater than unity, and the wood sinks.

47. HYDROSTATIC BALANCE.

Apparatus. A complete apparatus for this purpose, known as Mohr's Balance, may be obtained, and the following description is especially applicable to it. A common balance may, however, be substituted, raising one scale-pan and attaching a hook below. Instead of riders it is then generally more convenient to use ordinary weights. Some solids and liquids are also needed as substances whose specific gravity is to be determined.

Experiment. Attach the small scale-pan to the left, and the glass counterpoise to the right end of the beam. The weighing is done by riders, of which there are three sizes, whose weights are in the ratio 10, 100 and 1000. The beam is divided into 10 equal parts, so that when balanced the weight may be read off directly

to three places of decimals. Fill the small jar with water, and see what weight is necessary to immerse the counterpoise. It will be found to be very nearly 1000, and evidently equals the weight of the water displaced. Next, fill the jar with the liquid to be tested, and see what weights are now required. The ratio in the two cases is the specific gravity. The temperature should be recorded in each case by the thermometer contained in the counterpoise, and if great accuracy is required a correction applied for it, or better, the liquids may be cooled to the standard temperature.

To find the specific gravity of a solid, wind a piece of fine wire around it, and suspend from the left hand end of the beam. Counterpoise by adding lead, sand or paper to the scale-pan at the other end until a perfect balance is obtained. Immerse in a vessel of water, and balance by adding the riders; their weight equals that of an equal volume of water. Then remove the solid, and again bring the beam to a horizontal position by the riders; this gives the weight of the solid, which divided by the weight of the water displaced, gives the specific gravity. If more convenient, the weight of the body may be obtained directly by the riders without counterpoising it.

Next, find the specific gravity of a piece of wood, or other solid lighter than water. Attach a piece of lead, or other body heavy enough to sink it, and measure, as above, the following quantities. Weight of solid in air w, weight of lead in air w1, weight of lead in water w, weight of solid and lead in water w1. Then w W1 weight of a bulk of water equal to that of the lead. w1+ 20, W18 weight of a bulk of water equal to lead and solid. Hence their difference, or w1+w, W1s' = ws + wi weight of water equal in bulk to solid, and weight of solid divided

Is

8

Wis

The same precautions are necessary, as with the gauge flask, regarding air bubbles, and the riders should never be touched with the fingers, but always with a small bent wire.

Apparatus. In Fig. 41, A and B are two reservoirs of tin, or wooden boxes lined with lead, each containing two or three cubic

feet. Water is admitted by a valve at C, and passes through a cylinder of perforated tin D, to break up the stream and prevent much motion of the water in A. An outlet is made at E, which may be closed by a stick of wood with a rubber flap on its end K, which is held in place by the pressure of the water. To keep the level constant, a funnel F is connected with the interior by a rubber tube, so that it may be raised or lowered, and serve as an overflow, or a simple straight tube may be used, passing through the bottom of A to the surface. The height of the water is read by a hook gauge G with an index attached, moving over a scale. A number of brass plates fitting into E are provided with orifices of various shapes and sizes, some circular, rectangular and triangular, and others furnished with projecting cylindrical or conical tubes.

The second reservoir B has also a hook gauge and scale H to show the amount of water in it, and an outlet I closed by a plug. To prevent motion of the surface of the water around H, a diaphragm is placed in the centre of the reservoir, on which the water impinges, a number of holes being bored in the lower portion to equalize the level on each side.

Experiment. When water flows through an aperture in a thin plate the amount per minute is much less than that given by theory, owing to the contraction

Fig. 41.

H

B

cular orifices in E, and measure its height by bringing the water just on a level with it, and using the hook gauge. This is done as is described in Experiment 13, by bringing the point of the hook just to the surface of the liquid, so as slightly to distort the image of outside objects, and reading the position by the scale. Close E with the rod K and open the valve C, first raising the funnel F nearly to the top